It means “keep smelling” or “after taste/smell”.
It is the smell in the empty gaiwan after you have discarded the tea leaves and the gaiwan has cooled a little. Let your nose go deep into the gaiwan and smell the aroma that arises from the dried residue—it is heavenly and surprisingly different from the experience of smelling the steeped leaves themselves and from the smell of the tea.
I discovered this experience by accident during my tea classes while cleaning my covered bowls between different teas. The aroma wafting up at me before I poured hot water into the gaiwan to cleanse it was almost haunting. I didn’t realize that the Chinese had a name for it: liu xiang. I think it has some other names too, but liu xiang suits me fine.
Now, in addition to having class participants smell the steeped leaves, I pass around the empty gaiwan before cleaning it so everyone can get one more dimension from a leaf that just keeps giving.